The equivalent expression is 40c +100d . Therefore, 40c+100d is correct.
To find the equivalent expression for
10(4c+10d), you can distribute the factor 10 to both terms inside the parentheses. This involves multiplying 10 by each term:
10(4c+10d)=10⋅4c+10⋅10d.
Now, perform the multiplications:
=40c+100d.
So, the equivalent expression is 40c+100d.
You can also understand this by recognizing that distributing a factor to each term inside the parentheses is a fundamental property of algebra. In this case, the distributive property helps you break down the expression into the sum of two products:
a(b + c)= ab +ac.
In your expression, a=10, b=4c, and c=10d.
Applying the distributive property, you get 10(4c+10d)=10⋅4c+10⋅10d=40c+100d.
Therefore, the correct equivalent expression is 40c+100d.
Question
Which expression is equivalent to 10(4c+10d) ?
40c+100d
14c+10d
4c+100d
14c+14d